A note on boundary value problems on manifolds with cylindrical ends

Abstract. We present an extension of the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary, which prevents us from using the stan-dard characterization of Fredholm and compact (pseudo-)differential operators between Sobolev spaces on compact manifolds. As an application, we obtain a solution of the non-homogeneous Dirich-let problem in this setting. We also prove the existence of the Dirichlet-to-Neumann map in the class of pseudodifferential operators which are “almost translation invariant at infinity.